SOLUTION: solve the equation {{{2(10^y + 9)= 18-19(1-10^y)}}} y=? round answer to 3 decimal places

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Question 940462: solve the equation
2%2810%5Ey+%2B+9%29=+18-19%281-10%5Ey%29
y=?
round answer to 3 decimal places
Answer by laoman(51) About Me  (Show Source):
You can put this solution on YOUR website!

2%2810%5Ey+%2B+9%29=+18-19%281-10%5Ey%29
Let 10%5Ey+=+a
Therefore, let's substitute into the equation
2(a+9)=18-19(1-a)
2*a +18 = 18 -19+19*a
2*a-19*a = -1-18
-17*a= -19
a = 19/17
but 10^y = a
10^y = 19/17
Using logarith to solve
y*log 10 = log (19/17)
y= log (19/17)/log10
y = log(19/17) since log10 =1
y= 0.0483046
y= 0.048 ( to 3 d.p)
QED